Reducing the number of non-Clifford gates in quantum circuits

Abstract

We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations. This method matches or beats previous approaches to ancillae-free T-count reduction on the majority of our benchmark circuits, in some cases yielding up to 50% improvement. Our method begins by representing the quantum circuit as a ZX-diagram, a tensor networklike structure that can be transformed and simplified according to the rules of the ZX-calculus. We then extend a recent simplification strategy with a different ingredient, phase gadgetization, which we use to propagate non-Clifford phases through a ZX-diagram to find nonlocal cancellations. Our procedure extends unmodified to arbitrary phase angles and to parameter elimination for variational circuits. Finally, our optimization is self-checking, in the sense that the simplification strategy we propose is powerful enough to independently validate equality of the input circuit and the optimized output circuit. We have implemented the routines of this paper in the open-source library PyZX.

There and back again: A circuit extraction tale

“…Thus, this procedure is not only the most general circuit extraction algorithm for measurement patterns but also the most general known circuit extraction algorithm for ZX-diagrams. In particular, our algorithm can handle ZX-diagrams that contain phase gadgets [39], which have been used recently in a variety of circuit optimisation schemes [13,14,21].…”

“…Combined with the known procedure for transforming a quantum circuit into a measurement pattern using the ZX-calculus [26], our pattern simplification and circuit extraction procedure can be used to reduce the T-gate count of quantum circuits [39]. This involves translating the circuit into a ZX-diagram, transforming this to a diagram which corresponds to a measurement pattern, simplifying the pattern, and then re-extracting a circuit.…”

“…The name 'phase gadget' refers to a particular configuration of spiders in the ZXcalculus, which, in our setting, corresponds to spiders measured in the YZ plane. Phase gadgets have been used particularly in the study of circuit optimisation [13,21,39].…”

“…These measurement pattern rewrite rules, seen then as transformations of ZX-diagrams, were used in Ref. [39] to reduce the T-count of circuits. We will see how in our context they can be used to remove a qubit from a pattern, again while preserving determinism.…”

“…The algorithm described above uses the same idea as that described in Ref. [39]. But while they describe the procedure in terms of modifying a graph-like ZXdiagram, we describe it for MBQC+LC diagrams, a more general class of diagrams.…”